Why does my eyes get watery when I go outside under the sun? I don't look at the sun. 

Irritation. We call this "reactive epiphora" it is a natural reflex of the eye to stimulation and irritation. The best way to combat this is to use sunglasses. Yes, please don't look at the sun!
Sensitivity. No good answer- some people are just sensitive to the sun. Some have cataract which create a lot of glare and that glare can make some tear.
Sunlight can hurt. Although you may not be looking directly at the sun, the brightness can be almost painful - especially if you do not wear sunglasses. If the pain does not go away after a few seconds, or occurs even in room light, you should see your eye doctor. This can sometimes be caused by inflammation of the eye (iritis), which should be treated with eye drops.